Handbook of Civil Engineering Calculations

out introducing any significant error. Thus,
in Fig. 16, the soil prism OAB tends to
heave by sliding downward along OA under
active pressure and sliding upward along ab
against passive pressure. As stated earlier,
these planes of failure make an angle of a =
45° +
l
/2 with the principal planes.
Let b = width of footing; h = distance
from ground surface to bottom of footing; p
= soil pressure directly below footing. By
equating the total active and passive pres-
sures, state the following equation defining FIGURE 16
the conditions at impending failure:

w&(tan

5

a - tan a)

p = wh tan^4 a + + 2c (tan a + tan^3 a) (30)

2. Substitute numerical values; solve for b; evaluate p
   Thus, h = Q;p = 58/6; 0 = 15°; a = 45° + 7°30' = 52°30'; 58/b = 0.1056(3.759 - 1.303)74

• 2(1.2)(1.303 + 2.213); b = 6.55 ft (1.996 m);/? = 58,000/6.55 = 8850 lb/ft^2 (423.7 kPa).

SOIL CONSOLIDATIONAND CHANGE

IN VOID RATIO

In a laboratory test, a load was applied to a soil specimen having a height of 30 in (762.0
mm) and a void ratio of 96.0 percent. What was the void ratio when the load settled A in
(12.7mm)?

Calculation Procedure:

1. Construct a diagram representing the volumetric composition
   of the soil in the original and final states
   According to the Terzaghi theory of consolidation, the compression of a soil mass under
   an increase in pressure results primarily from the expulsion of water from the pores. At
   the instant the load is applied, it is supported entirely by the water, and the hydraulic gra-
   dient thus established induces flow. However, the flow in turn causes a continuous trans-
   fer of load from the water to the solids.
   Equilibrium is ultimately attained when the
   load is carried entirely by the solids, and the
   expulsion of the water then ceases. The time
   rate of expulsion, and therefore of consolida-
   tion, is a function of the permeability of the
   soil, the number of drainage faces, etc. Let H-
   original height of soil stratum; s = settlement;
   C 1 = original void ratio; e 2 = final void ratio.
   Using the given data, construct the diagram in
   Fig. 17, representing the volumetric composi-
   tion of the soil in the original and final states.

(a) Original state (b) Final state

FIGURE 17

Solids Solids

Voids Voids